I want to be able to use the Windows 7 built in Remote Desktop, and it works fine it seems while in my home network but that is relatively useless to be honest. Now when I tried connecting from the local library, expecting it to work, it wouldn't connect. I'm assuming there is a step I'm missing or a setting I have wrong. If someone could walk me through making this work I would be very grateful.

Probably ideal to setup a dynamic DNS service so you don't have to remember your WAN IP address constantly.

I use No-IP though I've also used DynDNS both work the same, just different domain name choices.

On your router you should first give the computer that's running Remote Desktop a static IP/DHCP Reservation. Then forward the port accordingly to that IP.

Though in the end, I think you'll be disappointed with Remote Desktop. Not really made for use over the Internet. I'd suggest VNC instead (many various "distributions" out there). Or the easiest, use LogMeIn